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A Hybrid Model for the Computationally-Efficient Simulation of the Cerebellar Granular Layer.

Cattani A, Solinas S, Canuto C - Front Comput Neurosci (2016)

Bottom Line: Specifically, in the discrete model, each cell is described by a set of time-dependent variables, whereas in the continuum model, cells are grouped into populations that are described by a set of continuous variables.By reconstructing the ensemble activity of the cerebellar granular layer network and by comparing our results to a more realistic computational network, we demonstrate that our description of the network activity, even though it is not biophysically detailed, is still capable of reproducing salient features of neural network dynamics.Our modeling approach yields a significant computational cost reduction by increasing the simulation speed at least 270 times.

View Article: PubMed Central - PubMed

Affiliation: Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems @UniTn, Istituto Italiano di Tecnologia Rovereto, Italy.

ABSTRACT
The aim of the present paper is to efficiently describe the membrane potential dynamics of neural populations formed by species having a high density difference in specific brain areas. We propose a hybrid model whose main ingredients are a conductance-based model (ODE system) and its continuous counterpart (PDE system) obtained through a limit process in which the number of neurons confined in a bounded region of the brain tissue is sent to infinity. Specifically, in the discrete model, each cell is described by a set of time-dependent variables, whereas in the continuum model, cells are grouped into populations that are described by a set of continuous variables. Communications between populations, which translate into interactions among the discrete and the continuous models, are the essence of the hybrid model we present here. The cerebellum and cerebellum-like structures show in their granular layer a large difference in the relative density of neuronal species making them a natural testing ground for our hybrid model. By reconstructing the ensemble activity of the cerebellar granular layer network and by comparing our results to a more realistic computational network, we demonstrate that our description of the network activity, even though it is not biophysically detailed, is still capable of reproducing salient features of neural network dynamics. Our modeling approach yields a significant computational cost reduction by increasing the simulation speed at least 270 times. The hybrid model reproduces interesting dynamics such as local microcircuit synchronization, traveling waves, center-surround, and time-windowing.

No MeSH data available.


Related in: MedlinePlus

Grid convergence for different structured grid resolutions of the continuous model for GrCs nodes. The total number of nodes is shown in the plot legend. The plot shows the sum of the GrC membrane potential ω over the entire surface shown in upper left panel of Figure 5, divided by the area of the grid pixel and plotted as a function of time. Notably, only the coarser grid resolution shows a visible difference from the other resolutions and the difference among the solutions reduces for prolonged time intervals.
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Figure 8: Grid convergence for different structured grid resolutions of the continuous model for GrCs nodes. The total number of nodes is shown in the plot legend. The plot shows the sum of the GrC membrane potential ω over the entire surface shown in upper left panel of Figure 5, divided by the area of the grid pixel and plotted as a function of time. Notably, only the coarser grid resolution shows a visible difference from the other resolutions and the difference among the solutions reduces for prolonged time intervals.

Mentions: Finally, we conclude the present section by stressing that the simulations provided in this paper turn out to be independent of the GrCs continuous population grid refinement. Indeed, focusing on the framework that describes the center-surround phenomenon, we exhibit a comparison among the solutions produced by the model with increasing number of nodes in the space discretization of the GrC population. In Figure 8, we show the evolution in time of the integral of the activity over the network domain for different values of the spatial resolution. In practice, all the grid refinements we checked are able to catch the correct dynamics with sufficient accuracy. Convergence is clearly documented, thereby providing a sound background to the use of our numerical simulator.


A Hybrid Model for the Computationally-Efficient Simulation of the Cerebellar Granular Layer.

Cattani A, Solinas S, Canuto C - Front Comput Neurosci (2016)

Grid convergence for different structured grid resolutions of the continuous model for GrCs nodes. The total number of nodes is shown in the plot legend. The plot shows the sum of the GrC membrane potential ω over the entire surface shown in upper left panel of Figure 5, divided by the area of the grid pixel and plotted as a function of time. Notably, only the coarser grid resolution shows a visible difference from the other resolutions and the difference among the solutions reduces for prolonged time intervals.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4837690&req=5

Figure 8: Grid convergence for different structured grid resolutions of the continuous model for GrCs nodes. The total number of nodes is shown in the plot legend. The plot shows the sum of the GrC membrane potential ω over the entire surface shown in upper left panel of Figure 5, divided by the area of the grid pixel and plotted as a function of time. Notably, only the coarser grid resolution shows a visible difference from the other resolutions and the difference among the solutions reduces for prolonged time intervals.
Mentions: Finally, we conclude the present section by stressing that the simulations provided in this paper turn out to be independent of the GrCs continuous population grid refinement. Indeed, focusing on the framework that describes the center-surround phenomenon, we exhibit a comparison among the solutions produced by the model with increasing number of nodes in the space discretization of the GrC population. In Figure 8, we show the evolution in time of the integral of the activity over the network domain for different values of the spatial resolution. In practice, all the grid refinements we checked are able to catch the correct dynamics with sufficient accuracy. Convergence is clearly documented, thereby providing a sound background to the use of our numerical simulator.

Bottom Line: Specifically, in the discrete model, each cell is described by a set of time-dependent variables, whereas in the continuum model, cells are grouped into populations that are described by a set of continuous variables.By reconstructing the ensemble activity of the cerebellar granular layer network and by comparing our results to a more realistic computational network, we demonstrate that our description of the network activity, even though it is not biophysically detailed, is still capable of reproducing salient features of neural network dynamics.Our modeling approach yields a significant computational cost reduction by increasing the simulation speed at least 270 times.

View Article: PubMed Central - PubMed

Affiliation: Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems @UniTn, Istituto Italiano di Tecnologia Rovereto, Italy.

ABSTRACT
The aim of the present paper is to efficiently describe the membrane potential dynamics of neural populations formed by species having a high density difference in specific brain areas. We propose a hybrid model whose main ingredients are a conductance-based model (ODE system) and its continuous counterpart (PDE system) obtained through a limit process in which the number of neurons confined in a bounded region of the brain tissue is sent to infinity. Specifically, in the discrete model, each cell is described by a set of time-dependent variables, whereas in the continuum model, cells are grouped into populations that are described by a set of continuous variables. Communications between populations, which translate into interactions among the discrete and the continuous models, are the essence of the hybrid model we present here. The cerebellum and cerebellum-like structures show in their granular layer a large difference in the relative density of neuronal species making them a natural testing ground for our hybrid model. By reconstructing the ensemble activity of the cerebellar granular layer network and by comparing our results to a more realistic computational network, we demonstrate that our description of the network activity, even though it is not biophysically detailed, is still capable of reproducing salient features of neural network dynamics. Our modeling approach yields a significant computational cost reduction by increasing the simulation speed at least 270 times. The hybrid model reproduces interesting dynamics such as local microcircuit synchronization, traveling waves, center-surround, and time-windowing.

No MeSH data available.


Related in: MedlinePlus